# Limit of a sequence

Hi,
Here is my dilemma: I am to prove that sin (n!*R*pi) has a limit, where R is a rational number. I rewrite R as a/b and I can see that whenever n=b, every subsequent term will be zero. I have tried to write this out using the definition of a limit, but I can't seem to break it down. I have been looking at these problems for a long time and I am blocked on this one.
CC

Physics Monkey
For a sequence $$a_n$$, we say that $$a_n \rightarrow L$$ if for every $$\epsilon > 0$$ we can find an $$N(\epsilon)$$ such that $$| a_n - L | < \epsilon$$ for $$n > N(\epsilon)$$.
You have guessed correctly that the limit is 0. Now I give you an $$\epsilon$$ and ask you to tell me where I should start looking so that the terms of the sequence are always closer than $$\epsilon$$ to the limit. Tell me where to look by giving me N. You've already pointed out that the terms of the sequence equal the limit beyond a certain point ...